integral from 2 to infinity of 5/(4+x^2)

Lösung

\int_{2}^{\infty} \frac{5}{4 + x ^{2}} d x

\frac{5 π}{8}

Dezimale

1.96349 \dots

Schritte zur Lösung

\int_{2}^{\infty} \frac{5}{4 + x ^{2}} d x

Berechne das unbestimmte Integral:

\int \frac{5}{4 + x ^{2}} d x = \frac{5}{2} arctan (\frac{x}{2}) + C

Berechne die Grenzen:

\int_{2}^{\infty} \frac{5}{4 + x ^{2}} d x = \frac{5 π}{4} - \frac{5 π}{8}

= \frac{5 π}{4} - \frac{5 π}{8}

Vereinfache

= \frac{5 π}{8}

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